Print medium displaying illusion image and non-transitory computer-readable recording medium holding illusion image data

ABSTRACT

The present invention obtains subband signals by performing a multiresolution decomposition by a wavelet frame with orientation selectivity or a filterbank with orientation selectivity that is a set of an approximate filter with no orientation and a plurality of detail filters with respective orientations on image data, and, when an image is reconstructed by summing the obtained subband signals, generates reconstructed image data that creates a floating illusion by attenuating or amplifying a subband signal corresponding to at least one of detail filters with a predetermined orientation relative to a floating direction, in which an image is desired to be floated due to an illusion, among the detail filters.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a continuation under 35 U.S.C. §111(a) ofco-pending U.S. application Ser. No. 13/874,641 filed on May 1, 2013,which is a continuation under 35 U.S.C. §111(a) of International PatentApplication No. PCT/JP2011/076747 filed on Nov. 15, 2011, anddesignating the U.S. among other countries, which claims the benefit offoreign priority to Japanese Patent Application No. JP 2010-254576 filedon Nov. 15, 2010, the disclosures of all of which are herebyincorporated by reference in their entireties. The InternationalApplication was published in Japanese on May 24, 2012, as InternationalPublication No. WO 2012/067254 A1 under PCT Article 21(2).

FIELD

The present invention relates to an illusion image generating apparatus,a medium, image data, an illusion image generating method, a printingmedium manufacturing method, and a program.

BACKGROUND

Conventionally, figures and the like that create an optical illusionhave been discovered. For example, illusion figures, such as a Hermanngrid, a Chevreul illusion, a Cafe Wall illusion, an Ouchi illusion, aPinna illusion, and a Gurnsey-Morgan illusion, have been discovered, andan illusion phenomenon is induced by viewing these illusion figures,illusions such as the size, position, color, or the like being perceiveddifferently from reality, a non-existent object being seen, and a stillimage appearing to move (see Non Patent Literature 1, 4, 5, 6, and 7).

Moreover, conventionally, wavelet frames with orientation selectivityreferred to as a pinwheel wavelet frame (see Non Patent Literature 3), asimple pinwheel framelet (see Non Patent Literature 2), and a pinwheelframelet have been developed as mathematical models of simple cells inthe human visual cortex, and are used for image analysis and the like.

CITATION LIST Non Patent Literature

Non Patent Literature 1: Hitoshi Arai “Illusion Figures”, Sanshusha Co.Ltd., 2007

Non Patent Literature 2: Hitoshi Arai and Shinobu Arai, “2D tightframelets with orientation selectivity suggested by vision science”,JSIAM Letters Vol. 1 (2009), pp. 9-12.

Non Patent Literature 3: Hitoshi Arai and Shinobu Arai, “Finitediscrete, shift-invariant, directional filterbanks for visualinformation processing, I: Construction”, Interdisciplinary InformationSciences, Vol. 13 (2007), pp. 255-273.

Non Patent Literature 4: Akiyoshi Kitaoka, “Illusion Introduction”,Asakura Publishing Co., Ltd., 2010

Non Patent Literature 5: Hajime Ouchi, Japanese Optical and GeometricalArt, Dover Publ. Inc., New York, (1973)

Non Patent Literature 6: B. Pinna and G. J. Brelstaff, “A new visualillusion of relative motion”, Vision Research 40 (2000), pp. 2091-2096.

Non Patent Literature 7: R. Gurnsey and G. Page (having an acute accenton the “e”), “Effects of local and global factors in the Pinnaillusion”, Vision Research 46 (2006), pp. 1823-1837.

SUMMARY Technical Problem

However, conventionally, illusion figures are discovered by accident orfound and generated in a highly skilled manner by using specificpatterns by illusion researchers, designers, or the like, which is aproblem in that there is no method of automatically generating anillusion image from an arbitrary image. In particular, although apinwheel framelet, a simple pinwheel framelet, and a pinwheel waveletframe are used, for example, for analyzing what causes the creation ofan illusion in an illusion figure, they are not used for generating anillusion image from an arbitrary image.

The present invention is achieved in view of the above problems and anobject of the present invention is to provide an illusion imagegenerating apparatus, a medium, image data, an illusion image generatingmethod, a printing medium manufacturing method, and a program capable ofgenerating an illusion image from an arbitrary image.

Solution to Problem

It is an object of the present invention to at least partially solve theproblems in the conventional technology. According to an aspect of thepresent invention, an illusion image generating apparatus includes atleast a storing unit and a control unit, wherein the storing unitincludes a filter storing unit that stores a wavelet frame withorientation selectivity or a filterbank with orientation selectivitythat is a set of an approximate filter with no orientation and aplurality of detail filters with respective orientations, and an imagedata storing unit that stores image data, the control unit includes adecomposing unit that obtains subband signals by performing amultiresolution decomposition by the wavelet frame with orientationselectivity or the filterbank with orientation selectivity on the imagedata, and a reconstructing unit that obtains reconstructed image data byreconstructing an image by summing the subband signals obtained by thedecomposing unit, and the reconstructing unit generates thereconstructed image data that creates a floating illusion by attenuatingor amplifying a subband signal corresponding to at least one of detailfilters with a predetermined orientation relative to a floatingdirection, in which an image is desired to be floated due to anillusion, among the detail filters.

According to another aspect of the present invention, in the illusionimage generating apparatus, the reconstructing unit attenuates a subbandsignal corresponding to at least one of detail filters with anorientation orthogonal or oblique to the floating direction, among thedetail filters.

According to still another aspect of the present invention, in theillusion image generating apparatus, the reconstructing unit attenuatesa subband signal corresponding to at least one of detail filtersbelonging to one group among two groups of a group composed of detailfilters with an orientation that is neither horizontal nor vertical toan orthogonal axis of the floating direction and is at a negative anglerelative to the orthogonal axis and a group composed of detail filterswith an orientation that is neither horizontal nor vertical to theorthogonal axis of the floating direction and is at a positive anglerelative to the orthogonal axis, and detail filters with an orientationorthogonal to the floating direction, among the detail filters.

According to still another aspect of the present invention, in theillusion image generating apparatus, the reconstructing unit attenuatesa subband signal corresponding to at least one of detail filters with anorientation that is tilted such that an absolute value of an anglerelative to the orthogonal axis is equal to or greater than 0° and lessthan or equal to 45°, among the detail filters belonging to the onegroup and the detail filters with the orientation orthogonal to thefloating direction.

According to still another aspect of the present invention, in theillusion image generating apparatus, the reconstructing unit attenuatesa subband signal corresponding to at least one of detail filters of upto a higher degree as the angle approaches 0° and up to a lower degreeas the angle approaches 45° among the detail filters with theorientation that is tilted such that an absolute value of an anglerelative to the orthogonal axis is equal to or greater than 0° and lessthan or equal to 45°.

According to still another aspect of the present invention, in theillusion image generating apparatus, the reconstructing unit amplifies asubband signal corresponding to at least one of detail filters belongingto another group among two groups of a group composed of detail filterswith an orientation that is neither horizontal nor vertical to anorthogonal axis of the floating direction and is at a negative anglerelative to the orthogonal axis and a group composed of detail filterswith an orientation that is neither horizontal nor vertical to theorthogonal axis of the floating direction and is at a positive anglerelative to the orthogonal axis, among the detail filters.

According to still another aspect of the present invention, in theillusion image generating apparatus, the reconstructing unit amplifies asubband signal corresponding to at least one of detail filters thatbelongs to the another group and has an orientation that is tilted suchthat an absolute value of an angle relative to the orthogonal axis is45°.

According to still another aspect of the present invention, in theillusion image generating apparatus, the reconstructing unit attenuatesor amplifies a subband signal such that images have floating directionsdifferent from each other, which include floating directions opposite toeach other, in image regions adjacent to each other in the reconstructedimage data.

According to still another aspect of the present invention, in theillusion image generating apparatus, the multiresolution decompositionby the decomposing unit is a maximal overlap multiresolutiondecomposition, a maximally decimated multiresolution decomposition, or apartially decimated and partially overlap multiresolution decomposition.

According to still another aspect of the present invention, a mediumdisplays an illusion image, wherein the illusion image is such that apredetermined component is attenuated or amplified among componentsextracted by filters with respective orientations or components withrespective orientations, which include wavelet components withrespective orientations, the components composing an original image.

According to still another aspect of the present invention, it relatesto an image data for displaying an illusion image, wherein the illusionimage is such that a predetermined component is attenuated or amplifiedamong components extracted by filters with respective orientations orcomponents with respective orientations, which include waveletcomponents with respective orientations, the components composing anoriginal image.

According to still another aspect of the present invention, it relatesto an illusion image generating method performed by an illusion imagegenerating apparatus that includes at least a storing unit and a controlunit, wherein the storing unit includes a filter storing unit thatstores a wavelet frame with orientation selectivity or a filterbank withorientation selectivity that is a set of an approximate filter with noorientation and a plurality of detail filters with respectiveorientations, and an image data storing unit that stores image data, themethod includes decomposing step of obtaining subband signals byperforming a multiresolution decomposition by the wavelet frame withorientation selectivity or the filterbank with orientation selectivityon the image data, and reconstructing step of obtaining reconstructedimage data by reconstructing an image by summing the subband signalsobtained in the decomposing unit, the decomposing step and thereconstructing step are performed by the control unit, and thereconstructing step includes generating the reconstructed image datathat creates a floating illusion by attenuating or amplifying a subbandsignal corresponding to at least one of detail filters with apredetermined orientation relative to a floating direction, in which animage is desired to be floated due to an illusion, among the detailfilters.

According to still another aspect of the present invention, it relatesto a printing medium manufacturing method performed by an illusion imagegenerating apparatus that includes at least a storing unit, a controlunit, and a printing unit, wherein the storing unit includes a filterstoring unit that stores a wavelet frame with orientation selectivity ora filterbank with orientation selectivity that is a set of anapproximate filter with no orientation and a plurality of detail filterswith respective orientations, and an image data storing unit that storesimage data, the method includes decomposing step of obtaining subbandsignals by performing a multiresolution decomposition by the waveletframe with orientation selectivity or the filterbank with orientationselectivity on the image data, reconstructing step of obtainingreconstructed image data by reconstructing an image by summing thesubband signals obtained in the decomposing unit, and illusion imageoutputting step of manufacturing a printing medium by outputting thereconstructed image data obtained in the reconstructing step to theprinting unit, the decomposing step, the reconstructing step, and theillusion image outputting step are performed by the control unit, andthe reconstructing step includes generating the reconstructed image datathat creates a floating illusion by attenuating or amplifying a subbandsignal corresponding to at least one of detail filters with apredetermined orientation relative to a floating direction, in which animage is desired to be floated due to an illusion, among the detailfilters.

According to still another aspect of the present invention, it relatesto a program that causes an illusion image generating apparatus thatincludes at least a storing unit and a control unit to execute anillusion image generating method, wherein the storing unit includes afilter storing unit that stores a wavelet frame with orientationselectivity or a filterbank with orientation selectivity that is a setof an approximate filter with no orientation and a plurality of detailfilters with respective orientations, and an image data storing unitthat stores image data, the program causes the control unit to executedecomposing step of obtaining subband signals by performing amultiresolution decomposition by the wavelet frame with orientationselectivity or the filterbank with orientation selectivity on the imagedata, and reconstructing step of obtaining reconstructed image data byreconstructing an image by summing the subband signals obtained in thedecomposing unit, and the reconstructing step includes generating thereconstructed image data that creates a floating illusion by attenuatingor amplifying a subband signal corresponding to at least one of detailfilters with a predetermined orientation relative to a floatingdirection, in which an image is desired to be floated due to anillusion, among the detail filters.

Moreover, the present invention is related to a recording medium, inwhich the above-described program is recorded.

Advantageous Effects of Invention

According to this invention, the illusion image generating apparatusstores a wavelet frame with orientation selectivity or a filterbank withorientation selectivity that is a set of an approximate filter with noorientation and a plurality of detail filters with respectiveorientations, and image data; obtains subband signals by performing amultiresolution decomposition by the wavelet frame with orientationselectivity or the filterbank with orientation selectivity on the imagedata, and; generates, when reconstructed image data is obtained byreconstructing an image by summing the obtained subband signals, thereconstructed image data that creates a floating illusion by attenuatingor amplifying a subband signal corresponding to at least one of detailfilters with a predetermined orientation relative to a floatingdirection, in which an image is desired to be floated due to anillusion, among the detail filters. Therefore, an illusion image can begenerated from an arbitrary image. More specifically, the presentinvention can create an illusion while maintaining representation of theoriginal image by effectively using the distribution of uniqueorientations that each original image has. Thus, the present inventioncan have various uses, i.e., the present invention can be applied tovarious original images.

Moreover, according to the present invention, the illusion imagegenerating apparatus attenuates a subband signal corresponding to atleast one of detail filters with an orientation orthogonal or oblique tothe floating direction, among the detail filters. Therefore, an illusionimage can be generated while maintaining representation of an arbitraryoriginal image.

Moreover, according to the present invention, the illusion imagegenerating apparatus attenuates a subband signal corresponding to atleast one of detail filters with an orientation belonging to one groupamong two groups of a group composed of detail filters with anorientation that is neither horizontal nor vertical to an orthogonalaxis of the floating direction and is at a negative angle relative tothe orthogonal axis and a group composed of detail filters with anorientation that is neither horizontal nor vertical to the orthogonalaxis of the floating direction and is at a positive angle relative tothe orthogonal axis, and detail filters with an orientation orthogonalto the floating direction, among the detail filters. Therefore,reconstructed image data in which a floating illusion is enhanced can begenerated.

Moreover, according to the present invention, the illusion imagegenerating apparatus attenuates a subband signal corresponding to atleast one of detail filters with an orientation that is tilted such thatan absolute value of an angle relative to the orthogonal axis of thefloating direction is equal to or greater than 0° and less than or equalto 45°, among the detail filters belonging to the one group and thedetail filters with the orientation orthogonal to the floatingdirection. Therefore, floating-illusion reconstructed image data can begenerated while further maintaining representation of an arbitraryoriginal image.

Moreover, according to the present invention, the illusion imagegenerating apparatus attenuates a subband signal corresponding to atleast one of detail filters of up to a higher degree as the angleapproaches 0° and up to a lower degree as the angle approaches 45° amongthe detail filters with the orientation that is tilted such that anabsolute value of an angle relative to the orthogonal axis of thefloating direction is equal to or greater than 0° and less than or equalto 45°. Therefore, floating-illusion reconstructed image data can begenerated while further maintaining representation of an arbitraryoriginal image.

Moreover, according to the present invention, the illusion imagegenerating apparatus amplifies a subband signal corresponding to atleast one of detail filters belonging to another group among two groupsof a group composed of detail filters with an orientation that isneither horizontal nor vertical to an orthogonal axis of the floatingdirection and is at a negative angle relative to the orthogonal axis anda group composed of detail filters with an orientation that is neitherhorizontal nor vertical to the orthogonal axis of the floating directionand is at a positive angle relative to the orthogonal axis, among thedetail filters. Therefore, reconstructed image data in which a floatingillusion is enhanced can be generated.

Moreover, according to the present invention, the illusion imagegenerating apparatus amplifies a subband signal corresponding to atleast one of detail filters that belongs to another group other than theone group among the two groups and has an orientation that is tiltedsuch that an absolute value of an angle relative to the orthogonal axisof the floating direction is 45°. Therefore, reconstructed image data inwhich a floating illusion is enhanced can be generated.

Moreover, according to the present invention, the illusion imagegenerating apparatus attenuates or amplifies a subband signal such thatimages have floating directions different from each other, such asfloating directions opposite to each other, in image regions adjacent toeach other in the reconstructed image data. Therefore, image regionsthat have floating directions different from each other, such asfloating directions opposite to each other, are adjacent to each other.Thus, reconstructed image data in which a floating illusion is furtherenhanced can be generated compared with the case where a subband signalcorresponding to a detail filter with the same orientation is attenuatedor amplified for all the image regions.

Moreover, according to the present invention, the multiresolutiondecomposition by the decomposing unit is a maximal overlapmultiresolution decomposition, a maximally decimated multiresolutiondecomposition, or a partially decimated and partially overlapmultiresolution decomposition. Therefore, a subband signal can beobtained by performing a preferable multiresolution decomposition.

Moreover, according to the present invention, in the medium thatdisplays an illusion image or the image data for displaying an illusionimage, the illusion image is such that a predetermined component isattenuated or amplified among components extracted by filters withrespective orientations or components with respective orientations, suchas wavelet components with respective orientations, which compose anoriginal image. Therefore, it is possible to provide an illusion imagegenerated from an arbitrary original image.

Moreover, according to the present invention, in the printing mediummanufacturing method, a wavelet frame with orientation selectivity or afilterbank with orientation selectivity that is a set of an approximatefilter with no orientation and a plurality of detail filters withrespective orientations and image data are stored. The printing mediummanufacturing method includes obtaining subband signals by performing amultiresolution decomposition by the wavelet frame with orientationselectivity or the filterbank with orientation selectivity on the imagedata; generating, when reconstructed image data is obtained byreconstructing an image by summing the obtained subband signals, thereconstructed image data that creates a floating illusion by attenuatingor amplifying a subband signal corresponding to at least one of detailfilters with a predetermined orientation relative to a floatingdirection, in which an image is desired to be floated due to anillusion, among the detail filters; and manufacturing a printing mediumby outputting the reconstructed image data to a printing unit.Therefore, a medium on which an illusion image generated from anarbitrary image is printed can be manufactured. More specifically, thepresent invention can manufacture a printing medium on which an illusionis created while maintaining representation of the original image byeffectively using the distribution of unique orientations that eachoriginal image has. Thus, the present invention can have various uses,i.e., the present invention can manufacture a printing medium on whichan illusion image applied to various original images is printed.

BRIEF DESCRIPTION OF DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 is a block diagram illustrating an example of the configurationof an illusion image generating apparatus to which the presentembodiment is applied.

FIG. 2 is a diagram illustrating an example of filters that are obtainedby calculating the cyclic correlation product of maximal overlappinwheel framelet filters at level 3 of degree 5 and maximal overlappinwheel framelet approximate filters at level 1 and level 2 of degree 5and that are for actually obtaining decomposition in the decompositionphase at level 3 in maximal overlap multiresolution decomposition by theframelets.

FIG. 3 is a diagram illustrating filters obtained by calculating thecyclic correlation product of maximal overlap pinwheel framelet filtersat level 2 (high frequency side) of degree 7 and a maximal overlappinwheel framelet approximate filter at level 1 of degree 7 and is adiagram for showing the difference depending on the level.

FIG. 4 is a diagram illustrating filters obtained by calculating thecyclic correlation product of maximal overlap pinwheel framelet filtersat level 3 (low frequency side) of degree 7 and maximal overlap pinwheelframelet approximate filters at level 1 and level 2 of degree 7 and is adiagram for showing the difference depending on the level.

FIG. 5 is a diagram in which the approximate part is represented bya_(k) and the detail parts are represented by symbols (numbers) ofd_(k)(1) to d_(k)(99) in the pinwheel framelet at level k of degree 7.

FIG. 6 is a diagram representing coefficients applied in associationwith the array of filters in FIG. 5.

FIG. 7 is a flowchart illustrating one example of the basic processingperformed by an illusion image generating apparatus 100 in the presentembodiment.

FIG. 8 is a diagram illustrating one example of the filterbanks in thedecomposition phase and the synthesis phase of maximal overlapmultiresolution decomposition.

FIG. 9 is a flowchart illustrating one example of the specificprocessing performed by the illusion image generating apparatus 100according to the present embodiment.

FIG. 10 is a diagram illustrating the original image of a grayscalecharacter string.

FIG. 11 is a diagram illustrating the processing table used in theprocessing method I-1.

FIG. 12 is a diagram illustrating the reconstructed image y obtained bythe processing method I-1.

FIG. 13 is a diagram illustrating the processing table used in aprocessing method I-2.

FIG. 14 is a diagram illustrating the reconstructed image y obtained bythe processing method I-2.

FIG. 15 is a diagram illustrating an illusion image generated byarranging the reconstructed images in FIG. 12 in odd rows and thereconstructed images in FIG. 14 in even rows.

FIG. 16 is a diagram illustrating the processing table used in aprocessing method II-1.

FIG. 17 is a diagram illustrating the reconstructed image y obtained bythe processing method II-1.

FIG. 18 is a diagram illustrating the processing table used in aprocessing method II-2.

FIG. 19 is a diagram illustrating the reconstructed image y obtained bythe processing method II-2.

FIG. 20 is a diagram illustrating an illusion image generated byarranging the reconstructed images in FIG. 17 in odd rows and thereconstructed images in FIG. 19 in even rows.

FIG. 21 is a diagram illustrating the original image of a colorillustration.

FIG. 22 is a diagram illustrating the reconstructed image obtained byprocessing the subband signals obtained from the original image in FIG.21 by the processing method II-1.

FIG. 23 is a diagram illustrating the reconstructed image obtained byprocessing the subband signals obtained from the original image in FIG.21 by the processing method II-2.

FIG. 24 is a diagram illustrating the reconstructed image obtained byprocessing the subband signals obtained from the original image in FIG.21 by the processing method I-1.

FIG. 25 is a diagram illustrating the reconstructed image obtained byprocessing the subband signals obtained from the original image in FIG.21 by the processing method I-2.

FIG. 26 is a diagram illustrating the processing table used in aprocessing method V-1-1 for generating an illusion image in which imageregions waver laterally in opposite directions to each other when beingmoved longitudinally.

FIG. 27 is a diagram illustrating the processing table used in aprocessing method V-1-2 for generating an illusion image in which imageregions waver laterally in opposite directions to each other when beingmoved longitudinally.

FIG. 28 is a diagram illustrating the processing table used in aprocessing method V-2-1 for generating an illusion image in which imageregions waver longitudinally in opposite directions to each other whenbeing moved laterally.

FIG. 29 is a diagram illustrating the processing table used in aprocessing method V-2-2 for generating an illusion image in which imageregions waver longitudinally in opposite directions to each other whenbeing moved laterally.

FIG. 30 is a diagram illustrating the processing table used in aprocessing method V-3-1 for generating an illusion image in which imageregions waver laterally in opposite directions to each other when beingmoved longitudinally.

FIG. 31 is a diagram illustrating the processing table used in aprocessing method V-3-2 for generating an illusion image in which imageregions waver laterally in opposite directions to each other when beingmoved longitudinally.

FIG. 32 is a diagram illustrating the processing table used in aprocessing method V-4-1 for generating an illusion image in which imageregions waver longitudinally in opposite directions to each other whenbeing moved laterally.

FIG. 33 is a diagram illustrating the processing table used in aprocessing method V-4-2 for generating an illusion image in which imageregions waver longitudinally in opposite directions to each other whenbeing moved laterally.

FIG. 34 is a diagram illustrating the processing table used in aprocessing method V-5-1 for generating a floating illusion image thatwavers laterally when being moved longitudinally and waverslongitudinally when being moved laterally.

FIG. 35 is a diagram illustrating the processing table used in aprocessing method V-5-2 for generating a floating illusion image thatwavers laterally when being moved longitudinally and waverslongitudinally when being moved laterally.

FIG. 36 is a diagram illustrating an illusion image generated by theprocessing method I.

FIG. 37 is a diagram illustrating an illusion image generated by theprocessing method V-5.

FIG. 38 is a diagram illustrating an example of an illusion imageobtained by arranging two reconstructed images alternatively in odd rowsand even rows and combining the images, where the two reconstructedimage are generated by using the processing tables between which theorientations are inverted relative to each other with respect to theaxis.

FIG. 39 is a diagram illustrating an example of an illusion imageobtained by arranging images such that images in one of the odd rows andthe even rows are shifted by ½ of the image length.

FIG. 40 is a diagram illustrating an example of an illusion imageobtained by arranging images such that images in one of the odd rows andthe even rows are shifted by ½ of the image length.

FIG. 41 is a diagram in which illusion images that are prepared forgenerating circular arrays and waver laterally in opposite directionsare arranged one above the other.

FIG. 42 is a diagram illustrating an illusion figure that appears torotate when approaching or moving away from the figure.

FIG. 43 is a diagram illustrating a floating illusion image that isprepared for generating circular arrays and wavers longitudinally whenbeing moved laterally.

FIG. 44 is a diagram illustrating an illusion image that expands andcontracts when being rotated.

FIG. 45 is a diagram illustrating the processing table used in aprocessing method VI-1 for generating an image that creates, when beingmoved in an oblique direction, illusions of wavering in obliquedirections that are orthogonal to the above oblique direction andopposite to each other.

FIG. 46 is a diagram illustrating the processing table used in aprocessing method VI-2 for generating an image that creates, when beingmoved in an oblique direction, illusions of wavering in obliquedirections that are orthogonal to the above oblique direction andopposite to each other.

FIG. 47 is a diagram illustrating an illusion image generated by theprocessing methods VI-1 and VI-2 such that adjacent image regions waverin opposite directions to each other.

FIG. 48 is a diagram illustrating a flowchart of the specific processingimproved by this example.

FIG. 49 is a diagram illustrating the result obtained by performing thescale conversion by the method in which a threshold is used in theabove-described specific processing.

FIG. 50 is a diagram illustrating the result obtained by performing thescale conversion under the condition where A is 15 and B is 85 in thisexample.

FIG. 51 is a histogram of L* for an image after the processing in StepSB-3 and before the processing in Step SB-4 in the specific processingperformed on an input image for the output images in FIG. 49 and FIG.50.

FIG. 52 is a histogram of L* for an image (FIG. 49) obtained byperforming the scale conversion on the image after the processing inStep SB-3 simply by using a threshold.

FIG. 53 is a histogram of L* for an image (FIG. 50) obtained byperforming the scale conversion on the image after the processing inStep SB-3 under the condition where A is 15 and B is 85 in this example.

FIG. 54 is a diagram illustrating the filters obtained by calculatingthe cyclic correlation product of maximum overlap pinwheel frameletfilters at level 2 of degree 7 and a maximal overlap pinwheel frameletapproximate filter at level 1 of degree 7.

FIG. 55 is a diagram illustrating each subband signal of the resultobtained by performing up to the 2nd stage of maximal overlapmultiresolution decomposition by a pinwheel framelet of degree 7 on atest image.

DESCRIPTION OF EMBODIMENTS

Embodiments of an illusion image generating apparatus, a medium, imagedata, an illusion image generating method, a printing mediummanufacturing method, and a program according to the present inventionwill be described in detail below with reference to the drawings. Thisinvention is not limited to the embodiments.

[Illusion Image]

An illusion image according to the medium and the image data in thepresent embodiment will be described below. Specifically, the medium inthe present embodiment is a medium that displays an illusion image andis a medium that permanently displays an illusion image, such as aprinting medium (paper, an OHP sheet, or the like) on which an illusionimage is printed. The image data in the present embodiment is image datafor displaying an illusion image and is, for example, two-dimensionalimage data in a raster format or a vector format.

The illusion image according to the medium and the image data in thepresent embodiment has the following characteristics. Specifically, theillusion image is characterized in that a predetermined component amongthe components that make up the original image and that are extracted byfilters with respective orientations is attenuated or amplified.Alternatively, the illusion image is characterized in that apredetermined component among the components with respectiveorientations, such as wavelet components with respective orientations,that make up the original image is attenuated or amplified.

As an example, such an illusion image is an illusion image that createsan illusion of floating due to the movement of the image or the viewerand is formed as a design, a photograph, and/or a character by having aregion formed by the light and dark (brightness), tone, or shades ofcolors in the image. In other words, the illusion image appears to movedifferently from the actual movement accompanied by the movement of theviewer or the movement of the image. The original image may be any imagerepresenting, for example, a design, a photograph, or a character.

In the present embodiment, the “wavelet” is not limited to a classicalwavelet, a wavelet in a narrow sense, and the like and includes awavelet in a broad sense. For example, the wavelet is a finite-lengthwaveform or a wave-like oscillation with an amplitude that amplifiesfrom zero and quickly converges to zero, and, for example, includespseudo wavelets, such as a Gabor filter and a curvelet.

Moreover, the “filters with respective orientations” are, for example, aplurality of detail filters with respective orientations. Components,such as subband signals for example, are extracted by the filters.

A component of a predetermined orientation that is attenuated may be,for example, at least one of the components of an orientation that isorthogonal or oblique to the floating direction. A component of apredetermined orientation that is attenuated is not limited to this andmay be at least one of the components of orientations that belong to oneof two groups, i.e., a group of orientations that are neither horizontalnor vertical to the orthogonal axis of the floating direction and are ata negative angle relative to the orthogonal axis and a group oforientations that are neither horizontal nor vertical to the orthogonalaxis of the floating direction and are at a positive angle relative tothe orthogonal axis, and the components of an orientation orthogonal tothe floating direction, among a plurality of orientations. Morespecifically, a component of a predetermined orientation that isattenuated may be at least one of the components of orientations thatare tilted such that the absolute value of the angle relative to theorthogonal axis is equal to or greater than 0° and less than or equal to45°, among the orientations belonging to one group and the orientationorthogonal to the floating direction. Still more specifically, acomponent of a predetermined orientation that is attenuated may be atleast one of the components of orientations that include those up to ahigher degree as the angle approaches 0° and those up to a lower degreeas the angle approaches 45° among the orientations that are tilted suchthat the absolute value of the angle relative to the orthogonal axis isequal to or greater than 0° and less than or equal to 45°.

Conversely, a component of a predetermined orientation that is amplifiedmay be at least one of the components of orientations that belong to theother of the two groups, i.e., the group of orientations that areneither horizontal nor vertical to the orthogonal axis of the floatingdirection and are at a negative angle relative to the orthogonal axisand the group of orientations that are neither horizontal nor verticalto the orthogonal axis of the floating direction and are at a positiveangle relative to the orthogonal axis, among a plurality oforientations. More specifically, a component of a predeterminedorientation that is amplified may be at least one of the components oforientations that belong to the other group and are tilted such that theabsolute value of the angle relative to the orthogonal axis is 45°.

In the illusion image, a component of a predetermined orientation may beattenuated or amplified such that image regions adjacent to each otherhave floating directions different from each other, such as floatingdirections opposite to each other. Consequently, the floating illusionis enhanced.

This is the end of the explanation of the illusion image according tothe medium and the image data in the present embodiment. The illusionimage according to the medium and the image data may be generated by anillusion image generating apparatus, an illusion image generatingmethod, a printing medium manufacturing method, or the like described inthe following embodiment.

[Configuration of Illusion Image Generating Apparatus]

Next, the configuration of the illusion image generating apparatus willbe described with reference to FIG. 1. FIG. 1 is a block diagramillustrating an example of the configuration of the illusion imagegenerating apparatus to which the present embodiment is applied andschematically illustrates only a portion relating to the presentembodiment in the configuration.

In FIG. 1, an illusion image generating apparatus 100 schematicallyincludes a control unit 102, a communication control interface unit 104,an input/output control interface unit 108, and a storing unit 106. Thecontrol unit 102 is a CPU or the like that performs overall control ofthe illusion image generating apparatus 100. The input/output controlinterface unit 108 is an interface connected to an input device 112 andan output device 114. Moreover, the storing unit 106 is a device thatstores various databases, tables, and the like. These units of theillusion image generating apparatus 100 are communicatively connectedvia an arbitrary communication channel.

Various files (a framelet file 106 a and an image data file 106 b)stored in the storing unit 106 are storage units, such as a fixed diskdrive. For example, the storing unit 106 stores various programs,tables, files, databases, web pages, and the like used for variousprocessings.

Among these components of the storing unit 106, the framelet file 106 ais a filter storing unit that stores wavelet frames with orientationselectivity or filterbanks with orientation selectivity, which are eacha set of an approximate filter with no orientation and a plurality ofdetail filters with respective orientations. In the present embodiment,a pinwheel framelet is used as a wavelet frame with orientationselectivity; however, the wavelet frame with orientation selectivity isnot limited to this and, for example, a simple pinwheel framelet (seeNon Patent Literature 2), a pinwheel wavelet frame (see Non PatentLiterature 3), or the like may be used. Whereas a pinwheel wavelet frameis such that the length of the filters composing the frame changes inaccordance with the number of pixels of the original image, a pinwheelframelet and a simple pinwheel framelet have a property where the lengthof the filters is independent of the number of pixels. For example, apinwheel framelet is a two-dimensional framelet with orientationselectivity and is one type of a multiwavelet frame. A pinwheel frameletis, for example, a mathematical model of simple cells in the humanvisual cortex. This decomposition is a mathematical model of signalsdecomposed by simple cells in the human brain. A pinwheel framelet is amodel neuroscientifically closer to simple cells in V1 of the cerebralcortex than a simple pinwheel framelet. A pinwheel framelet, forexample, has a degree that is an odd number of three or greater. Thelarger the degree, the more the orientations can be detected. A pinwheelframelet has a property where the number of filters increases and thecalculation time increases as the degree increases. Moreover, the numberof filters of a pinwheel framelet of degree n is, for example,(n+1)²+(n−1)². Among them, one filter is an approximate filter and theremaining filters are detail filters. FIG. 2 illustrates filtersobtained by calculating the cyclic correlation product of maximaloverlap pinwheel framelet filters at level 3 of degree 5 and maximaloverlap pinwheel framelet approximate filters at level 1 and level 2 ofdegree 5 (for example of the cyclic correlation product, see HitoshiArai, “Linear Algebra, Basics and Applications”, Nippon hyoron sha Co.,Ltd. (2006)).

Because the degree of this pinwheel framelet is 5, for example, asillustrated FIG. 2, the pinwheel framelet is composed of a set of 52filters in total, i.e., 6×6 filters on the left side and 4×4 filters onthe right side, for each level. Among them, one filter surrounded by ablack rectangle in the central upper portion in FIG. 2 is a filterobtained by calculating the cyclic correlation product of theapproximate filters from level 1 to level 3, and the other 51 filtersare filters obtained by calculating the cyclic correlation product ofthe detail filters at level 3 and the approximate filters from level 1to level 2. The orientations of the filters generated by the detailfilters are arranged substantially in the direction in which a pinwheelrotates around the filter generated only from the approximate filters.As will be described later, maximal overlap multiresolutiondecomposition by using a pinwheel framelet of each degree has levels,and level 1 detects the finest portion (high frequency portion). FIG. 2illustrates the pinwheel framelet at level 3, and approximate portions(low frequency portions) are detected as the level increases to 2, 3, .. . . The framelet file 106 a may store wavelet frames with orientationselectivity, such as a pinwheel framelet, in the form of a function(such as a frequency response function of framelet filters). A specificexample of the function will be described later.

Various wavelets may be used in the present embodiment without beinglimited to the above. The wavelet is not limited to a classical wavelet,a wavelet in a narrow sense, and the like and includes a wavelet in abroad sense. For example, the wavelet is a finite-length waveform or awave-like oscillation with an amplitude that amplifies from zero andquickly converges to zero, and, for example, includes pseudo wavelets,such as a Gabor filter and a curvelet. Moreover, the framelet file 106 amay store a filter group, such as a filterbank with orientationselectivity, and filters with orientations without being limited to aframe, such as a wavelet frame with orientation selectivity.

The image data file 106 b is an image data storing unit that storesimage data. The image data stored in the image data file 106 b may be,for example, image data input via the input device 112 or may be imagedata received from an external system 200 or the like via a network 300.Moreover, the image data may be image data for a color image or may begrayscale image data. An image (data) before being subjected tomultiresolution decomposition by wavelet frames with orientationselectivity, such as a pinwheel framelet, is referred to as the originalimage (data) and an image (data) after being reconstructed on the basisof subband signals is referred to as a reconstructed image (data). Theimage data file 106 b may store, as image data, a unit impulse signalfor an image size (the number of pixels) that is the same as that of theimage data for the target original image. The unit impulse signal storedin the image data file 106 b is input to the filterbank stored in theframelet file 106 a as image data in a similar manner and the outputunit impulse response is used for high-speed calculation of the imagedata for the target original image. A high-speed calculation method willbe described in detail later.

Here the description returns to FIG. 1 again. The input/output controlinterface unit 108 controls the input device 112 and the output device114. As the output device 114, a display device, such as a monitor(including a domestic television), a printing device, such as printer,and the like can be used. Moreover, as the input device 112, a keyboard,a mouse, a microphone, or the like can be used in addition to an imagingdevice, such as a camera, an input device connected to an externalstorage medium, and the like.

Moreover, in FIG. 1, the control unit 102 includes an internal memoryfor storing a control program, such as an OS (Operating system), aprogram defining various processing procedures and the like, andrequired data. The control unit 102 performs information processing forperforming various processings by these programs or the like. Thecontrol unit 102 includes a decomposing unit 102 a, a reconstructingunit 102 b, a color space conversion unit 102 d, and an illusion imageoutput unit 102 e on the basis of functional concept. The reconstructingunit 102 b further includes a floating illusion creating unit 102 c.

Among them, the decomposing unit 102 a is a decomposing unit thatobtains subband signals by performing multiresolution decomposition onimage data by using wavelet frames with orientation selectivity, such asa pinwheel framelet, or filterbanks with orientation selectivity storedin the framelet file 106 a. The “multiresolution decomposition” includesmaximal overlap multiresolution decomposition, maximally decimatedmultiresolution decomposition, and partially decimated and partiallyoverlap multiresolution decomposition (for example of maximal overlapmultiresolution decomposition, see Hitoshi Arai, “Wavelet”, KyoritsuShuppan Co., Ltd. (2010)). When multiresolution decomposition iscalculated by the decomposing unit 102 a, the cyclic correlation productand the cyclic convolution product are used; however, it may becalculated by a well-known high-speed calculation method in which a fastFourier transform is used. As described above, multiresolutiondecomposition by wavelet frames with orientation selectivity, such as apinwheel framelet, has levels. FIG. 3 and FIG. 4 are diagrams forshowing the difference depending on the level of a pinwheel framelet.FIG. 3 illustrates filters obtained by calculating the cycliccorrelation product of maximal overlap pinwheel framelet filters atlevel 2 (high frequency side) and a maximal overlap pinwheel frameletapproximate filter at level 1. FIG. 4 illustrates filters obtained bycalculating the cyclic correlation product of maximal overlap frameletfilters at level 3 (low frequency side) and maximal overlap pinwheelframelet approximate filters at level 1 and level 2. Because the degreeof both of them is 7, the number of filters is (7+1)²+(7−1)²=100.

As an example, the decomposing unit 102 a first detects the finestportion (high frequency portion) by maximal overlap multiresolutiondecomposition by using a pinwheel framelet at level 1 and detectsapproximate portions (low frequency portions) as the level increases to2, 3, . . . .

Multiresolution decomposition by pinwheel framelets includes adecomposition phase and a synthesis phase. Each phase is composed of afilterbank composed of an array of approximate filters and detailfilters. After performing the image processing in the decompositionphase and the synthesis phase, the decomposing unit 102 a finallydecomposes the original image data into image signals (specifically,subband signals) the number of which is “the number of filters×levels”.

For example, in the case of maximal overlap multiresolutiondecomposition of 5 levels by using a pinwheel framelet of degree 7, thesubband signals at a certain level k (k=1 to 5) include 1 approximatepart obtained by 1 approximate filter and 99 detail parts obtained by 99detail filters. FIG. 5 is a diagram in which the approximate part isrepresented by a_(k) and the detail parts are represented by symbols(numbers) of d_(k)(1) to d_(k)(99) in the pinwheel framelet at level kof degree 7. The position of the symbol (number) is associated with theposition of each filter in FIG. 3 (k=2) or FIG. 4 (k=3). In other words,a_(k) and d_(k)(1) to d_(k)(99) represent the subband signals obtainedby the filters at the corresponding positions in FIG. 3 or FIG. 4.

Moreover, the reconstructing unit 102 b is a reconstructing unit thatobtains reconstructed image data by reconstructing an image by summingthe subband signals obtained by the decomposing unit 102 a. For example,the reconstructing unit 102 b obtains reconstructed image data byreconstructing an image by summing the subband signal of the approximatepart obtained by the approximate filter at the maximum level describedabove and the subband signals of the detail parts obtained by all thedetail filters. At this point, if the pinwheel framelet has a perfectreconstruction property and the floating illusion creating unit 102 c tobe described later does not perform any processing, the reconstructingunit 102 b reproduces an image that is the same as the original image.In other words, the reconstructing unit 102 b obtains reconstructedimage data that creates a floating illusion (differently from theoriginal image) by summing the subband signals after attenuating(deleting) or amplifying (enhancing) a specific subband signal by theprocessing performed by the floating illusion creating unit 102 c.

The relationship between the perfect reconstruction property and thefloating illusion creating processing will be described using thesymbols (numbers) described above. The perfect reconstruction propertyof maximal overlap multiresolution decomposition is expressed by thefollowing equation:x=a ₅+(d ₅(1)+ . . . +d ₅(99))+ . . . +(d ₁(1)+ . . . +d ₁(99))where x is the input signal (original signal) of the original image.

A coefficient of an appropriate real number is applied to each detailpart thus, b_(5,1), . . . , b_(5,99), . . . , b_(1,1), . . . , b_(1,99).FIG. 6 is a diagram representing coefficients applied in associationwith the array of filters in FIG. 5. In this case, the reconstructedimage (signal) is represented by the following equation:y=a ₅+(b _(5,1) d ₅(1)+ . . . +b _(5,99) d ₅(99))+ . . . +(b _(1,1) d₁(1)+ . . . +b _(1,99) d ₁(99))

At this point, if each coefficient b_(5,1)= . . . =b_(5,99)= . . .=b_(1,1)= . . . =b_(1,99)=1, then obviously x=y (the original image andthe reconstructed image are the same), which indicates a perfectreconstruction. In the present embodiment, as an example, the floatingillusion creating unit 102 c generates the reconstructed image thatcreates a floating illusion by setting the values b_(5,1), . . . ,b_(5,99), . . . , b_(1,1), . . . , b_(1,99) such that a floatingillusion can be created.

Before describing a subband signal that is attenuated or amplified so asto create a floating illusion, classification of the detail filters willbe described. The detail filters can be classified into five types onthe basis of their orientation. Specifically, if the axis orthogonal tothe floating direction, in which an image is desired to be floated dueto an illusion, is referred to as the “orthogonal axis”, the detailfilters can be classified into five types, i.e., a (1) detail filterwith an orientation in the same direction as the orthogonal axis, a (2)detail filter with an orientation in the direction vertical to theorthogonal axis, a (3) detail filter with an orientation that is at apositive angle relative to the orthogonal axis, a (4) detail filter withan orientation that is at a negative angle relative to the orthogonalaxis, and a (5) detail filter whose orientation is not uniquely defined.The angle θ relative to the orthogonal axis of the floating direction isrepresented by −90°<θ≦+90°, where the counterclockwise direction isdefined as the positive direction. The detail filter with an orientation(θ=0°, 90°) horizontal or vertical to the orthogonal axis is classifiedas (1) or (2) and therefore is not classified as (3) or (4). Moreover,the “(5) detail filter whose orientation is not uniquely defined”includes orientations at both a positive angle and a negative angle, theabsolute values of which relative to the orthogonal axis are the same;therefore, this detail filter is not classified as (3) or (4).

If the longitudinal direction is the floating direction, in the examplein FIG. 5, the subband signals corresponding to the “(1) detail filterwith an orientation in the same direction as the orthogonal axis” ared_(k)(15), d_(k)(23), d_(k)(31), d_(k)(39), d_(k)(47), d_(k)(55), andd_(k)(63). The subband signals corresponding to the “(2) detail filterwith an orientation in the direction vertical to the orthogonal axis”are d_(k)(1) to d_(k)(7). The subband signals corresponding to the “(3)detail filter with an orientation that is at a positive angle relativeto the orthogonal axis” are d_(k)(64) to d_(k)(99). The subband signalscorresponding to the “(4) detail filter with an orientation that is at anegative angle relative to the orthogonal axis” are d_(k)(9) tod_(k)(14), d_(k)(17) to d_(k)(22), d_(k)(25) to d_(k)(30), d_(k)(33) tod_(k)(38), d_(k)(41) to d_(k)(46), and d_(k)(49) to d_(k)(54). Thesubband signals corresponding to the “(5) detail filter whoseorientation is not uniquely defined” are d_(k)(8), d_(k)(16), d_(k)(24),d_(k)(32), d_(k)(40), d_(k)(48), and d_(k)(56) to d_(k)(62). The abovedescription is the explanation of the classification of the detailfilters.

The floating illusion creating unit 102 c is a floating illusioncreating unit that attenuates or amplifies a subband signalcorresponding to a detail filter with a predetermined orientation (aspecifically determined orientation) relative to the floating directionin which an image is desired to be floated due to an illusion.

In the present embodiment, as an example, the floating illusion creatingunit 102 c may generate reconstructed image data that creates a floatingillusion by attenuating the subband signal corresponding to the detailfilter with an orientation orthogonal to the floating direction in whichan image is desired to be floated due to an illusion, among a pluralityof the detail filters. Specifically, the floating illusion creating unit102 c may attenuate the subband signals corresponding to the “(1) detailfilter with an orientation in the same direction as the orthogonal axis”in the classification described above. For example, in FIG. 5, when animage is desired to be floated in the longitudinal direction (verticaldirection in FIG. 5) due to an illusion, the floating illusion creatingunit 102 c attenuates the subband signals of d_(k)(15), d_(k)(23),d_(k)(31), d_(k)(39), d_(k)(47), d_(k)(55), and d_(k)(63). Morespecifically, the floating illusion creating unit 102 c sets thecoefficients of b_(k,15), b_(k,23), b_(k,31), b_(k,39), b_(k,47),b_(k,55), and b_(k,63) to values equal to or greater than zero and lessthan one (see FIG. 6). In the subband signals generated by thedecomposing unit 102 a from the original image data, if the bias in thesignal strength is low between the subband signals corresponding to the“(3) detail filter with an orientation that is at a positive anglerelative to the orthogonal axis” and the subband signals correspondingto the “(4) detail filter with an orientation that is at a negativeangle relative to the orthogonal axis”, a floating illusion created bythe signal attenuation by the floating illusion creating unit 102 cusing this method is weak in some cases; however, the bias in the signalstrength can be amplified and thus the floating illusion can be enhancedby attenuating or amplifying a subband signal by further performing thefollowing method 1 or 2.

(Method 1: Attenuation of a Subband Signal in One Group Among TwoGroups)

In the method 1, the subband signal corresponding to at least one of thedetail filters belonging to one group is attenuated among two groups,i.e., the group composed of the “(3) detail filters with orientationsthat are at a positive angle relative to the orthogonal axis” and thegroup composed of the “(4) detail filters with orientations that are ata negative angle relative to the orthogonal axis”. Specifically, among aplurality of the detail filters, the floating illusion creating unit 102c may further attenuate the subband signal corresponding to at least oneof the detail filters belonging to one group among the two groups, i.e.,the group composed of the detail filters with orientations that areneither horizontal nor vertical to the orthogonal axis of the floatingdirection and are at a negative angle relative to the orthogonal axisand the group composed of the detail filters with orientations that areneither horizontal nor vertical to the orthogonal axis of the floatingdirection and are at a positive angle relative to the orthogonal axis.More specifically, if the group composed of the “(4) detail filters withorientations that are at a negative angle relative to the orthogonalaxis” is defined as “one group”, the floating illusion creating unit 102c sets the coefficient of at least one of b_(k,9) to b_(k,14), b_(k,17)to b_(k,22), b_(k,25) to b_(k,30), b_(k,33) to b_(k,38), b_(k,41) tob_(k,46), and b_(k,49) to b_(k,54) corresponding to the one group to avalue equal to or greater than zero and less than one.

When the range of the subband signals to be attenuated is furtherlimited, it is possible to attenuate the subband signal corresponding toat least one of the detail filters with orientations that are tiltedsuch that the absolute value of the angle relative to the orthogonalaxis is greater than 0° and less than or equal to 45°, among the detailfilters belonging to one group. More specifically, if the group composedof the “(4) detail filters with orientations that are at a negativeangle relative to the orthogonal axis” is “one group”, the floatingillusion creating unit 102 c sets the coefficient of at least one ofb_(k,14), b_(k,21), b_(k,22), b_(k,28) to b_(k,30), b_(k,35) tob_(k,38), b_(k,42) to b_(k,46), and b_(k,49) to b_(k,54) to a valueequal to or greater than zero and less than one.

When the range of the subband signals to be attenuated is still furtherlimited, it is possible to attenuate the subband signal corresponding toat least one of the detail filters that include those up to a higherdegree as the angle approaches 0° and those up to a lower degree as theangle approaches 45°, among the detail filters with orientations thatare tilted such that the absolute value of the angle relative to theorthogonal axis is greater than 0° and less than or equal to 45°. Morespecifically, if the group composed of the “(4) detail filters withorientations that are at a negative angle relative to the orthogonalaxis” is “one group”, the floating illusion creating unit 102 c sets thecoefficient of at least one of b_(k,14), b_(k,21), b_(k,22), b_(k,28) tob_(k,30), b_(k,36) to b_(k,38), b_(k,45), b_(k,46), and b_(k,54) to avalue equal to or greater than zero and less than one. As describedabove, if the subband signal corresponding to at least one of the detailfilters belonging to one group is attenuated, some of the subbandsignals corresponding to the detail filters with an orientationorthogonal to the floating direction may not be attenuated.

(Method 2: Amplification of a Subband Signal in the Other of Two Groups)

In the method 2, the subband signal corresponding to at least one of thedetail filters belonging to the other group (the group that is differentfrom the one group in the method 1) is amplified among two groups, i.e.,the group composed of the “(3) detail filters with orientations that areat a positive angle relative to the orthogonal axis” and the groupcomposed of the “(4) detail filters with orientations that are at anegative angle relative to the orthogonal axis”. For example, thefloating illusion creating unit 102 c amplifies the subband signalcorresponding to the detail filter that belongs to the other group amongthe two groups and has an orientation of 45° relative to the orthogonalaxis of the floating direction. More specifically, if the group composedof the “(3) detail filters with orientations that are at a positiveangle relative to the orthogonal axis” is “the other group”, thefloating illusion creating unit 102 c sets the coefficients of b_(k,64),b_(k,71), b_(k,78), b_(k,85), b_(k,92), and b_(k,99) to a value greaterthan one to amplify the subband signals corresponding to the detailfilters of d_(k)(64), d_(k)(71), d_(k)(78), d_(k)(85), d_(k)(92), andd_(k)(99).

The above description is an example of a pattern of the subband signalsattenuated or amplified by the floating illusion creating unit 102 c. Inthe example of the symbols (numbers) and the coefficients with referenceto FIG. 5 described above, an explanation is given of the example wherethe longitudinal direction is the floating direction; however, if animage is desired to be floated in the lateral direction, it issufficient to attenuate or amplify the subband signals of the detailfilters of a pattern obtained by flipping the above pattern about a 45°axis in a similar manner (example will be described later). Moreover, inthe above example, an explanation is given of the example where thegroup composed of the “(4) detail filters with orientations that are ata negative angle relative to the orthogonal axis” is “one group” and thegroup composed of the “(3) detail filters with orientations that are ata positive angle relative to the orthogonal axis” is “the other group”;however, it is possible to attenuate or amplify the subband signals ofthe detail filters of a pattern obtained by inverting the right and leftparts of the above pattern by interchanging both groups in a similarmanner. In this case, the floating direction is reversed along the sameaxis. This can be used to enhance the floating illusion such that imagesfloat in opposite directions to each other in two adjacent imageregions.

In other words, the floating illusion creating unit 102 c may controlthe orientations of the detail filters that attenuate or amplify subbandsignals such that the floating directions are opposite to each other inthe image regions adjacent to each other in the reconstructed imagedata. In other words, because there are detail filters in which theabsolute value of the angle is the same between the “(3) detail filterswith orientations that are at a positive angle relative to theorthogonal axis” and the “(4) detail filters with orientations that areat a negative angle relative to the orthogonal axis”, it is sufficientto interchange positive and negative signs of the angle of theorientations of the detail filters for the targets to be attenuated oramplified between two adjacent image regions. For example, in one imageregion, when the subband signals of d_(k)(64), d_(k)(71), d_(k)(78),d_(k)(85), d_(k)(92), and d_(k)(99) are amplified as in the aboveexample, the floating illusion creating unit 102 c amplifies the subbandsignals corresponding to the detail filters of d_(k)(14), d_(k)(21),d_(k)(28), d_(k)(35), d_(k)(42), and d_(k)(49) in the other image regionadjacent to the one image region. The floating illusion creating unit102 c may divide the original image data into two or more image regionsand then amplify or attenuate the corresponding subband signals in eachimage region. Moreover, the floating illusion creating unit 102 c mayamplify or attenuate the corresponding subband signals in the data ofthe same or different two or more original images and then combine theimages.

Here the description returns to FIG. 1 again. The color space conversionunit 102 d is a color space conversion unit that performs conversion ofthe color space, decomposition and synthesis of the color components,and the like. For example, when the image data stored in the image datafile 106 b is a color image, the color space conversion unit 102 dconverts the color space to the CIELAB color space before processing isperformed by the decomposing unit 102 a. Consequently, the image isdecomposed into three color components, i.e., L* (brightness), a*(red-green), and b* (yellow-blue). The color space conversion unit 102 dmay convert the color space to other color spaces other than the CIELABcolor space. The advantage of using the CIELAB color space is that onlybrightness information can be used as an input signal for thedecomposing unit 102 a. When the image data is grayscale, the colorspace conversion unit 102 d does not need to perform processing relatingto the color space.

Moreover, the illusion image output unit 102 e outputs, to the outputdevice 114, reconstructed image data reconstructed by the reconstructingunit 102 b while attenuating or amplifying subband signals by thefloating illusion creating unit 102 c after causing the color spaceconversion unit 102 d to perform synthesis of the color components,conversion of the color space, scale conversion of the brightness andcolor, and the like if necessary. For example, the illusion image outputunit 102 e may display and output a reconstructed image to a displaydevice, such as a monitor, or print output a reconstructed image to aprinting device, such as a printer, and create a printing medium. Themedium that is a printing target may be, for example, paper, an OHPsheet, or the like, or may be in the form of, for example, a flyer, afan, a card, a picture book, a New Year's card, a Christmas card, abusiness card, or the like. The illusion image output unit 102 e maychange the design (for example, the size is changed to postcard size orthe like) depending on its intended use according to the output form.Moreover, the illusion image output unit 102 e may transmit areconstructed image data to the external system 200 via the network 300.

In other words, the illusion image generating apparatus 100 may becommunicatively connected to the network 300 via a communication device,such as a router, and a wired or wireless communication line, such as adedicated line. In FIG. 1, the communication control interface unit 104performs communication control between the illusion image generatingapparatus 100 and the network 300 (or a communication device, such as arouter). In other words, the communication control interface unit 104 isan interface connected to a communication device (not shown), such as arouter, connected to a communication line or the like, and has afunction of performing data communication with other terminals viacommunication lines. In FIG. 1, the network 300 has a function ofmutually connecting the illusion image generating apparatus 100 and theexternal system 200 and is, for example, the Internet or the like.

In FIG. 1, the external system 200 is mutually connected to the illusionimage generating apparatus 100 via the network 300 and may have afunction of providing a program for causing an external databaserelating to image data or a pinwheel framelet or a computer to functionas the illusion image generating apparatus. The external system 200 maybe configured as a WEB server, an ASP server, or the like. Moreover, thehardware configuration of the external system 200 may be composed of aninformation processing apparatus, such as commercially availableworkstation and personal computer, and accessory devices thereof. Thefunctions of the external system 200 are realized by a CPU, a diskdevice, a memory device, an input device, an output device, acommunication control device, and the like in the hardware configurationof the external system 200, programs for controlling these devices, andthe like.

This is the end of the explanation of the configuration of the illusionimage generating apparatus 100 according to the present embodiment.

[Processing by Illusion Image Generating Apparatus 100]

Next, one example of the processing performed by the illusion imagegenerating apparatus 100 according to the present embodiment configuredas above will be described in detail below with reference to FIG. 7 toFIG. 53.

[Basic Processing]

First, the basic processing performed by the illusion image generatingapparatus 100 will be described with reference to FIG. 7 and FIG. 8.FIG. 7 is a flowchart illustrating one example of the basic processingperformed by the illusion image generating apparatus 100 in the presentembodiment.

First, the decomposing unit 102 a obtains subband signals by performingmaximal overlap multiresolution decomposition by using the pinwheelframelets stored in the framelet file 106 a on the image data stored inthe image data file 106 b (Step SA-1). FIG. 8 is a diagram illustratingone example of the filterbanks in the decomposition phase and thesynthesis phase of maximal overlap multiresolution decomposition. Thenumbers in FIG. 8 indicate levels. “PW” indicates a detail filter. Inthe case of degree 7, 99 detail filters are present for each level. “A”indicates an approximate filter. In the case of degree 7, oneapproximate filter is present for each level.

As illustrated in FIG. 8, first, the decomposing unit 102 a decomposesthe original image as an input signal into signals that pass 99 detailfilters and a signal that passes 1 approximate filter by using thepinwheel framelet at level 1. Next, the decomposing unit 102 adecomposes the signal that has passed the approximate filter at level 1into signals that pass 99 detail filters (at level 2) and a signal thatpasses 1 approximate filter (at level 2) by using the pinwheel frameletat level 2. The decomposing unit 102 a repeats this processing until thelevel reaches the maximum level (in the case of FIG. 8, at level 5).Then, the decomposing unit 102 a puts the signals obtained in thedecomposition phase through the filterbank in the synthesis phase andfinally obtains 99×5 subband signals (detail parts) and 1 subband signal(approximate part).

Here the description returns to FIG. 7 again. The reconstructing unit102 b does not perfectly reconstruct the image by simply summing thesubband signals obtained by the decomposing unit 102 a in the abovemanner but creates a floating illusion on the reconstructed image databy attenuating or amplifying subband signals from detail filters of aspecific pattern by the processing performed by the floating illusioncreating unit 102 c (Step SA-2). In the present embodiment, asillustrated in FIG. 8, the floating illusion creating unit 102 cperforms processing on the subband information by multiplying thesubband signals output from the decomposing unit 102 a by coefficients.A specific example of a pattern of detail filters that attenuate oramplify subband signals will be described in detail in the next section.

Then, the reconstructing unit 102 b reconstructs the image by summingthe subband signals processed by the floating illusion creating unit 102c as above (Step SA-3).

Then, the basic processing performed by the illusion image generatingapparatus 100 ends.

[Specific Processing]

Next, details of the processing that further specifically explain thebasic processing performed by the illusion image generating apparatus100 will be described with reference to FIG. 9 to FIG. 47. FIG. 9 is aflowchart illustrating one example of the specific processing performedby the illusion image generating apparatus 100 according to the presentembodiment. For this specific processing, an explanation will be givenof color space conversion processing and decomposition and synthesisprocessing of color components necessary for a color image, processingof designing reconstructed image data depending on the intended use,printing processing for obtaining finished products, and the like inaddition to the specific examples of the basic processing describedabove.

(Step SB-1)

First, a user prepares the original image (such as a character string,an illustration, or a photograph) that is desired to be floated due toan illusion and stores it in the image data file 106 b via the inputdevice 112 or the like.

When the stored image data is a color image, the illusion imagegenerating apparatus 100 converts the color space to the CIELAB colorspace by the processing performed by the color space conversion unit 102d. Consequently, the image is decomposed into three color components,i.e., L* (brightness), a* (red-green), and b* (yellow-blue). When theimage data is grayscale, the color space conversion unit 102 d does notperform processing relating to the color space.

(Step SB-2)

Then, the decomposing unit 102 a performs maximal overlapmultiresolution decomposition by using pinwheel framelets on each colorcomponent (one color in the case of grayscale) of the original imagethat is an input signal. In this embodiment, an explanation is givenwhen pinwheel framelets of degree 7 are used; however, similar imageprocessing can be performed also by using wavelet frames of otherdegrees or with different orientation selectivity. As other examples, asimple pinwheel framelet may be used (see Non Patent Literature 2).Alternatively, a pinwheel wavelet frame can also be used (see Non PatentLiterature 3). Moreover, multiresolution decomposition, such asmaximally decimated multiresolution decomposition or partially decimatedand partially overlap multiresolution decomposition, may be performedwithout being limited to maximal overlap multiresolution decomposition.

(Step SB-3)

Then, the reconstructing unit 102 b does not sum all the subband signalsobtained by performing maximal overlap multiresolution decomposition bythe decomposing unit 102 a but performs processing of deleting certainsubband signals, adding certain subband signals without modifying them,and adding certain subband signals after amplifying them by the floatingillusion creating unit 102 c. A floating illusion image is obtained byarranging the images each obtained by processing the original image bythis processing method. Examples of a processing method will bedescribed below by classifying them into some cases. In the followingexamples, the floating illusion creating unit 102 c increases or reducessubband signals by setting the coefficients b_(k,n) illustrated in FIG.6. No operation is performed on the coefficient a_(k) of the approximatepart (a_(k)=A=1).

(I) Processing Method for Creating an Illusion of Longitudinal Waveringwhen an Image is Moved Laterally Using a Grayscale Character String

An explanation will be given of, for example, the processing method forgenerating an illusion image that wavers longitudinally when being movedlaterally by processing the Kanji character string which means “JapanScience and Technology Agency” as illustrated in FIG. 10. The illusionimage can be generated in a similar manner with other character strings.In this example, the subband signals are amplified or attenuated byprocessing the images in FIG. 10 by processing methods I-1 and I-2 suchthat the images have floating directions opposite to each other and thenthe images are combined, thereby enhancing the floating illusion byfloating the images in opposite directions along the same axis in twoadjacent image regions. FIG. 11 is a diagram illustrating the processingtable used in the processing method I-1. The positions of thecoefficients in FIG. 6 correspond to the positions of the values in theprocessing table illustrated below.

In terms of the values 0, 1, and 2 in the processing table, the value 0means that the corresponding subband signal is multiplied by 0, i.e., isdeleted, the value 1 means that the corresponding subband signal ismultiplied by 1, i.e., is not processed, and the value 2 means that thecorresponding subband signal is amplified by a factor of 2. For example,because the value at the position of the coefficient b_(k,l) of thedetail part d_(k)(1) at level k in the processing table is one, nochange is made to d_(k)(1). Because the value at the positioncorresponding to b_(k,9) in the processing table is zero, d_(k)(9) isdeleted. Because the value at the position corresponding to b_(k,64) inthe processing table is two, d_(k)(64) is doubled.

The reconstructing unit 102 b obtains the reconstructed image y, whichcreates a floating illusion, by setting the values in the processingtable illustrated in FIG. 11 used in the processing method I-1 ascoefficient values by the floating illusion creating unit 102 c. FIG. 12is a diagram illustrating the reconstructed image y obtained by theprocessing method I-1. Even a single reconstructed image y becomes anillusion image that wavers longitudinally when being moved laterally.FIG. 13 is a diagram illustrating the processing table used in theprocessing method I-2.

As illustrated in FIG. 13, the pattern in the processing table used inthe processing method I-2 is such that the orientations of the targetdetail filters are set to be an inversion of to those in the pattern inthe processing table used in the processing method I-1 about the axis inthe longitudinal direction. In other words, the positive and negativesigns of the angle of the orientations of the target detail filters thatattenuate or amplify the subband signals are interchanged. FIG. 14 is adiagram illustrating the reconstructed image y obtained by theprocessing method I-2. This single reconstructed image y waverslongitudinally when being moved laterally and floats in the directionopposite to the reconstructed image y in FIG. 12 along the same axis.

Through the use of this property, the reconstructing unit 102 bgenerates an illusion image in which the floating illusion is enhancedas illustrated in FIG. 15 by arranging the reconstructed images in FIG.12 in odd rows and arranging the reconstructed images in FIG. 14 in evenrows. In other words, because the character strings of adjacent imageregions waver in opposite directions to each other, an image in whichthe illusion is enhanced can be obtained. In the above example,processing is performed up to level 5; however, the number of levelsappropriate for a floating illusion changes depending on the size andthe like of an image. Processing up to a lower level generates an imagethat is not far removed from the original image; however, if the numberof levels is too small, the amount of illusion becomes small.

(II) Processing Method for Creating an Illusion of Lateral Wavering whenan Image is Moved Longitudinally Using a Grayscale Character String

In the above (I), an explanation is given of the processing method forcreating an illusion of longitudinal wavering when an image is movedlaterally. Next, an explanation will be given of a processing method forcreating an illusion of lateral wavering when an image is movedlongitudinally. In this example also, the subband signals are amplifiedor attenuated by processing the images in FIG. 10 by processing methodsII-1 and II-2 and then the images are combined, thereby enhancing thefloating illusion by floating the images in opposite directions to eachother along the same axis in two adjacent image regions. FIG. 16 is adiagram illustrating the processing table used in the processing methodII-1.

The reconstructing unit 102 b obtains the reconstructed image y, whichcreates a floating illusion, by setting the values in the processingtable illustrated in FIG. 16 used in the processing method II-1 ascoefficient values by the floating illusion creating unit 102 c. FIG. 17is a diagram illustrating the reconstructed image y obtained by theprocessing method II-1. Even a single reconstructed image y becomes anillusion image that wavers laterally when being moved longitudinally.FIG. 18 is a diagram illustrating the processing table used in theprocessing method II-2.

As illustrated in FIG. 18, the pattern in the processing table used inthe processing method II-2 is such that the orientations of the targetdetail filters are set to be an inversion of those in the pattern in theprocessing table used in the processing method II-1 about the axis inthe longitudinal direction. In other words, the positive and negativesigns of the angle of the orientations of the target detail filters thatattenuate or amplify the subband signals are interchanged. FIG. 19 is adiagram illustrating the reconstructed image y obtained by theprocessing method II-2. This single reconstructed image y waverslaterally when being moved longitudinally and floats in the directionopposite to the reconstructed image y in FIG. 17 along the same axis.

Through the use of this property, the reconstructing unit 102 bgenerates an illusion image in which the floating illusion is enhancedas illustrated in FIG. 20 by arranging the reconstructed images in FIG.17 in odd rows and arranging the reconstructed images in FIG. 19 in evenrows. In other words, because the character strings of adjacent imageregions waver in opposite directions to each other, an image in whichthe illusion is enhanced can be obtained.

The above description is an explanation of the processing examples (I)and (II) of the grayscale character string. In the case of grayscale,brightness is expressed by 256 levels between 0 and 255; however, thevalue of the brightness after the processing exceeds the range of 0 to255 in some cases. In such a case, two types of display methodsperformed by the illusion image output unit 102 e are considered. One isthe method (normalizing method) of making the value fall within therange of 0 to 255 by scaling the entire range of the gray scale values.The above character string is displayed by this method. The other methodis the method (method in which a threshold is used) of setting any valueless than or equal to 0 to 0 and replacing any value equal to or greaterthan 255 with 255.

(III) Processing Method for Creating an Illusion of Lateral Waveringwhen an Image is Moved Longitudinally Using a Color Image

An explanation will be given of a processing method for creating anillusion of lateral wavering when an image is moved longitudinally usinga color image. In the case of a color image, first, the color spaceconversion unit 102 d converts the original image to the color spaceCIELAB so as to decompose the image into the components, i.e., L*(brightness), a* (red-green), and b* (yellow-blue), which are processingtargets. The processing target may be selected depending on the intendeduse, such as processing only L* (brightness) and processing all of L*,a*, and b*.

For example, the amount of illusion increases in the case of processingall of L*, a*, and b* compared with the case of processing only L*;however, an image becomes more different from the original image in thecase of processing all of L*, a*, and b* than the case of processingonly L*. The processing method can be selected depending on whether theemphasis is put on the image quality being close to the original imageor increasing the amount of illusion. Moreover, before actuallydisplaying and outputting or printing out the image by the illusionimage output unit 102 e, the color space conversion unit 102 dsynthesizes the image signals of the processed color components so as torestore the image to a color image (Step SB-4). Conversion to the colorspace sRGB or the like may be performed if necessary.

In this embodiment, as an example, a method for creating a floatingillusion from the original image that is a color illustration in FIG. 21will be described. A floating illusion can be created in a similarmanner also from other images (color photograph or the like). In asimilar manner to the case of the floating illusion of the characterstring described above, the floating illusion creating unit 102 cperforms the two processing methods II-1 and II-2 for creating illusionsof floating in opposite directions to each other. FIG. 22 is a diagramillustrating the reconstructed image obtained by processing the subbandsignals obtained from the original image in FIG. 21 by the processingmethod II-1. FIG. 23 is a diagram illustrating the reconstructed imageobtained by processing the subband signals obtained from the originalimage in FIG. 21 by the processing method II-2. In this example, themaximum level is six and only L* (brightness) is processed. The displaymethod by the illusion image output unit 102 e is in accordance with theabove-described method in which a threshold is used.

(IV) Processing Method for Creating an Illusion of Longitudinal Waveringwhen an Image is Moved Laterally Using a Color Image

In a similar manner, the processing method for creating an illusion oflongitudinal wavering when an image is moved laterally from the colorimage in FIG. 21 will be described. In a similar manner to the floatingillusion of the above-described character string, the floating illusioncreating unit 102 c performs the two processing methods I-1 and I-2 forcreating illusions of floating in opposite directions to each other.FIG. 24 is a diagram illustrating the reconstructed image obtained byprocessing the subband signals obtained from the original image in FIG.21 by the processing method I-1. FIG. 25 is a diagram illustrating thereconstructed image obtained by processing the subband signals obtainedfrom the original image in FIG. 21 by the processing method I-2. In thisexample also, the maximum level is six and only L* (brightness) isprocessed.

(V) Other Variations of the Processing Table

Examples of a processing method and a processing table different fromthe above-described processing methods will be described. FIG. 26 andFIG. 27 are diagrams illustrating the processing tables used inprocessing methods V-1-1 and V-1-2 for generating an illusion image inwhich image regions waver laterally in opposite directions to each otherwhen being moved longitudinally. FIG. 28 and FIG. 29 are diagramsillustrating the processing tables used in processing methods V-2-1 andV-2-2 for generating an illusion image in which image regions waverlongitudinally in opposite directions to each other when being movedlaterally. M₁ to M₆ are real numbers equal to or greater than one andare preferably around two. In this example, in the detail filters thatbelong to one group among two groups, i.e., the group composed of the“(3) detail filters with orientations that are at a positive anglerelative to the orthogonal axis” and the group composed of the “(4)detail filters with orientations that are at a negative angle relativeto the orthogonal axis”, the subband signals are deleted that correspondto the detail filters that include those up to a higher degree as theangle approaches 0° and those up to a lower degree as the angleapproaches 45° among the detail filters with orientations that aretilted greater than 0° and less than or equal to 45° relative to theorthogonal axis of the floating direction.

Although the illusion effect is relatively low, these processing methodsV-1 and V-2 can reproduce an image closer to the original image. In theprocessing method V-2-1 and the processing method V-2⁻², if M₁= . . .=M₆=1, it is possible to generate the reconstructed image obtained byremoving illusion components from the original image of a characterstring tilted illusion.

As a contrast, an explanation will be given, with reference to FIG. 30to FIG. 33, of examples of a processing method and a processing tablewith which the reconstructed image becomes relatively different from theoriginal image even though the amount of illusion increases. FIG. 30 andFIG. 31 are diagrams illustrating the processing tables used inprocessing methods V-3-1 and V-3-2 for generating an illusion image inwhich image regions waver laterally in opposite directions to each otherwhen being moved longitudinally. FIG. 32 and FIG. 33 are diagramsillustrating the processing tables used in processing methods V-4-1 andV-4-2 for generating an illusion image in which image regions waverlongitudinally in opposite directions to each other when being movedlaterally. In this example, the subband signals corresponding to all thedetail filters with orientations that belong to one group among the twogroups (3) and (4) are deleted. If M₁= . . . =M₆=2, the processingtables become the same as the processing tables used in the processingmethods I and II.

An explanation will be given, with reference to FIG. 34 to FIG. 35, ofother examples of a processing table with which the reconstructed imagebecomes different from the original image even though the illusion isenhanced. FIG. 34 and FIG. 35 are diagrams illustrating the processingtables used in processing methods V-5-1 and V-5-2 for generating afloating illusion image that wavers laterally when being movedlongitudinally and waver longitudinally when being moved laterally. Asillustrated in FIG. 34 and FIG. 35, in this example, in order to setboth the longitudinal direction and the lateral direction as thefloating direction, the subband signals corresponding to the detailfilters with an orientation in the longitudinal direction and the detailfilters with an orientation in the lateral direction are deleted. Theprocessing methods V-1 to 5 are representative examples of variationsand a processing table that interpolates the processing methods V-1 to 5may be used.

FIG. 36 is a diagram illustrating the illusion image generated by theprocessing method I and FIG. 37 is a diagram illustrating the illusionimage generated by the processing method V-5. As illustrated in FIG. 37,the illusion image in FIG. 37 wavers laterally when being movedlongitudinally and wavers longitudinally when being moved laterally dueto an illusion. However, the shape of the characters is different fromthe original image compared with FIG. 36 by the processing method I.

(VI) Processing Method for Creating an Illusion of Floating in anOblique Direction

The above-described examples use the processing tables that create anillusion of wavering in the right and left (lateral) direction when animage is moved up and down (longitudinally) or an illusion of waveringin the up and down (longitudinal) direction when an image is moved rightand left (laterally), and an explanation will be given of an example of,when an image is moved in an oblique direction (for example, θ=+45°),creating an illusion of wavering in an oblique direction (for example,θ=−45° orthogonal to the above direction. FIG. 45 and FIG. 46 arediagrams illustrating the processing tables used in processing methodsVI-1 and VI-2 for generating an image that creates, when being moved inan oblique direction, illusions of wavering in oblique directions thatare orthogonal to the above direction and are opposite to each other.

As illustrated in FIG. 45 and FIG. 46, the processing tables used in theprocessing methods VI-1 and VI-2 are tables obtained by rotating theprocessing tables (M₁= . . . =M₆=2) used in the processing methods V-5-1and V-5-2 illustrated in FIG. 34 and FIG. 35 for 45° in clockwisedirection. In other words, the orientations of the target detail filtersthat attenuate or amplify the subband signals are shifted by 45°.

FIG. 47 is a diagram illustrating the illusion image generated by theprocessing methods VI-1 and VI-2 such that color illustrations ofadjacent image regions waver in opposite directions to each other. Asillustrated in FIG. 47, when this illusion image is moved in an obliquedirection, the image appears to float in the direction vertical to theoblique direction. In this manner, it is possible to change thedirection in which an image floats by shifting the orientations of thetarget detail filters that attenuate or amplify the subband signals byan arbitrary angle in the processing table described above. This can beused to enhance the floating illusion such that images float indifferent directions other than the directions opposite to each other inadjacent image regions.

(Step SB-5)

As described above with the character strings and the colorillustrations as examples, the floating illusion is enhanced byarranging images such that the floating directions due to an illusionare opposite to each other in adjacent image regions. For example, thereconstructing unit 102 b combines images by arranging two reconstructedimages that are generated by the floating illusion creating unit 102 cusing the processing tables between which the positive and negativesigns of the angle of the orientations are interchanged, alternativelyin odd rows and even rows (see FIG. 38). The arranging method is notlimited to this and various arranging methods are considered. Forexample, the images may be arranged such that the images in one of theodd rows and the even rows are shifted by ½ of the image length (seeFIG. 39 and FIG. 40). Moreover, the floating illusion may be enhanced byarranging images such that, in adjacent image regions, the floatingdirections due to an illusion are different from each other, with thefloating directions not being limited to the directions opposite to eachother.

Moreover, images may be arranged in a circle and are not limited tobeing arranged in parallel. First, as illustrated in FIG. 41, imagesthat waver laterally in opposite directions when being movedlongitudinally are arranged one above the other to enhance the illusion.In this example, although the figures are shifted laterally by ½ of thefigure between the upper and lower stages, this is for design reasonsand is not essential. Then, when the appropriate number of the images inFIG. 41 are concentrically arranged, as illustrated in FIG. 42, it ispossible to generate an illusion figure with which the circular arraysappear to rotate alternately when approaching or moving away from thefigure. In the example in FIG. 42, the images in FIG. 41 are reducedlogarithmically toward the center. Moreover, a polar coordinateconversion is used for arranging the images in circles.

When the floating illusion images (FIG. 43) that waver longitudinallywhen being moved laterally are arranged in circles, as illustrated inFIG. 44, an illusion image that appears to expand and contract whenbeing rotated can be generated.

This is the end of the explanation of the specific processing performedby the illusion image generating apparatus 100.

[Example of High-Speed Calculation Method]

In the example of the specific processing described above with referenceto FIG. 9, a large number of filtering calculations needs to beperformed to calculate the processing in Steps SB-2 and SB-3 every timean image is input; therefore, a relatively long time is required. Inthis example, an example of a high-speed calculation method thatshortens the filtering calculation time will be explained.

First, the control unit 102 (the decomposing unit 102 a, thereconstructing unit 102 b, and the like) inputs an unit impulse signalfor an image size (the number of pixels), which is the same as that ofthe image signal, to a filterbank to be used (for example, theabove-described filterbank in FIG. 8) instead of the image signal andstores in advance an output signal F in the storing unit 106, such asthe framelet file 106 a. The unit impulse signal is, for example, asignal in which the value of the upper left end is one and other valuesare all zero in the image signal.

Then, when a floating illusion image is generated, the control unit 102calculates the cyclic convolution product x*F (also referred to as thecircular convolution product) of an image x, on which the processing inStep SB-1 explained with reference to FIG. 9 is performed, and F (forexample of the cyclic convolution product, see Hitoshi Arai, “FourierAnalysis”, Asakura Publishing Co., Ltd. (2003)). The calculated x*Fbecomes the same as the reconstructed image y calculated by the specificprocessing described above with reference to FIG. 9.

In this manner, through the use of the high-speed calculation method ofcalculating the convolution product of the precalculated impulseresponse and the original image, when floating illusion images with thesame image size (the number of pixels) are generated by the sameprocessing method for a plurality of original images, the time and theamount of calculation can be considerably reduced. More specifically, inthe example of the specific processing explained with reference to FIG.9, 25 seconds are required to generate a floating illusion image for oneoriginal image; however, through the use of the high-speed calculationmethod, a floating illusion image can be generated in 2 seconds for oneoriginal image by precalculating the impulse response F (although ittakes 23 seconds to calculate F).

[Scale Conversion of Brightness and Color]

In the example of the specific processing explained above with referenceto FIG. 9, an explanation is given of an example where, when the imagedata is a color image, the color space is converted to the CIELAB colorspace by the processing performed by the color space conversion unit 102d and L* (brightness) is set as a processing target in Step SB-1. Then,for Step SB-4, an explanation is mainly given of an example of applyingthe method in which a threshold is used that, when the value of thebrightness after the processing exceeds the range of 0 to 255, sets avalue less than or equal to 0 to 0 and replaces a value equal to orgreater than 255 with 255. In this example, an explanation will be givenof a method of the scale conversion of the brightness and color that canincrease the amount of illusion or make an image more visible dependingon the image by appropriately converting the scale of the brightness andcolor. FIG. 48 is a diagram illustrating a flowchart of the specificprocessing improved by this example. In this example, all of L*, a*, andb*, which are obtained by converting the color space to the CIELAB colorspace in Step SB-1, are set as a processing target.

As illustrated in FIG. 48, in this example, in Step SB-4, processing ofthe scale conversion of the brightness and color is added. Theprocessing of the scale conversion of the brightness and color performedby the color space conversion unit 102 d is as follows.

That is, as described above, the control unit 102 performs theprocessing (high-speed calculation method may be used) in Steps SB-2 andSB-3 on all of L*, a*, and b* as a processing target. At this point, inthe original image, for example, the values of L* are in the range ofequal to or greater than 0 and equal to or less than 100; however, thevalues of L* of the image after the processing do not always fallbetween 0 and 100; therefore, if any processing is not performed, thevalue that is out of the range of equal to or greater than 0 and equalto or less than 100 is not displayed.

In this example, in Step SB-4, the color space conversion unit 102 dperforms the following scale conversion without applying the method inwhich a threshold is used. Specifically, A and B, which satisfies0<A<B<100 are set in advance. The color space conversion unit 102 dperforms conversion as follows. That is, if the value after theprocessing is equal to or less than A, the color space conversion unit102 d replaces the value with A; if the value after the processing isequal to or greater than B, the color space conversion unit 102 dreplaces the value with B; and if the value after the processing is in arange of equal to or greater than A and less than or equal to B, thecolor space conversion unit 102 d increases or decreases the value suchthat the value falls within the range of equal to or greater than 0 andless than or equal to 100. The following linear equation, for example,may be used as the conversion method.

$\left. x\rightarrow{\frac{100}{B - A}\left( {x - A} \right)} \right.$

In the above description, the scale conversion is performed on thevalues of L*; however, the scale conversion may be performed in asimilar manner also on the values of a* and b*. FIG. 49 is a diagramillustrating the result obtained by performing the scale conversion bythe method in which a threshold is used in the above-described specificprocessing. FIG. 50 is a diagram illustrating the result obtained byperforming the scale conversion under the condition where A is 15 and Bis 85 in this example.

It can be seen that the image in FIG. 50 in this example has a largeramount of illusion and is more clear than the image in FIG. 49. Anexplanation will be given of a comparison of the histograms of thebrightness values. FIG. 51 is a histogram of L* for an image after theprocessing in Step SB-3 and before the processing in Step SB-4 in thespecific processing. FIG. 52 is a histogram of L* for an image obtainedby performing the scale conversion on the image after the processing inStep SB-3 simply by using a threshold. FIG. 53 is a histogram of L* foran image obtained by performing the scale conversion on the image afterthe processing in Step SB-3 under the condition where A is 15 and B is85 in this example.

As illustrated in FIG. 51, in the image before the scale conversionprocessing, some values exceed 100. When the scale conversion isperformed in this example (FIG. 53), the brightness peaks at a highervalue than the case of performing a simple scale conversion using athreshold (FIG. 52); therefore, the entire image becomes bright.Moreover, according to this example, because the spread of thedistribution becomes large, the gradation is clear and the amount ofillusion is increased. In this manner, if the scale conversion isperformed by the method in this example, effects are obtained where animage becomes more visible or the amount of illusion is increaseddepending on the image. Because each image has a suitable scaleconversion method, the values of A and B can be arbitrarily selecteddepending on the image.

[Pinwheel Framelet]

In the present embodiment, as described above, a pinwheel framelet to beused as an example may be a wavelet frame with orientation selectivity,such as well-known simple pinwheel framelet or pinwheel wavelet frame,or a filterbank with orientation selectivity. A pinwheel framelet willbe described below.

For the symmetric matrix given by A=(A_(k,l)):(n+1)×(n+1), a matrix thatsatisfies A_(s,t)=A_(n-s,t)=A_(s,n-t)=A_(n-s,n-t)=s is determined, wheredegree n is odd and n≧3, s=0, 1, . . . , [n/2], and t=s, . . . , [n/2].[ ] is Gauss symbol.

If n=7, the following matrix satisfies the condition.

$A = \begin{pmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 \\0 & 1 & 2 & 2 & 2 & 2 & 1 & 0 \\0 & 1 & 2 & 3 & 3 & 2 & 1 & 0 \\0 & 1 & 2 & 3 & 3 & 2 & 1 & 0 \\0 & 1 & 2 & 2 & 2 & 2 & 1 & 0 \\0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$

If the matrix is given by B=(B_(k,l)):(n+1)×(n+1), B is a matrixsatisfying the following condition (P).

$\mspace{20mu}{{{Condition}\;(P)}:\left\{ {{\begin{matrix}{B_{k,l} = B_{l,k}} \\{B_{k,l} = {B_{{n - k},l} = {B_{k,{n - 1}} = B_{{n - k},{n - 1}}}}} \\{B_{k,l} \geq 0}\end{matrix}\mspace{20mu} n_{0}} = {{\left\lbrack \frac{n}{2} \right\rbrack\mspace{14mu}{there}\mspace{14mu}{are}\mspace{14mu}\frac{1}{2}\;\left( {n_{0} + 1} \right)\left( {n_{0} + 3} \right)\mspace{14mu}{free}\mspace{14mu}{{variables}.{F_{k,l}^{1}\left( {\theta_{1},\theta_{2}} \right)}}} = {{\frac{1}{2}{{\det\; M}}^{1/2}i^{k + l + A_{k,l}}{\mathbb{e}}^{{- \pi}\;{\mathbb{i}}\;\theta_{1}}{\mathbb{e}}^{{- \pi}\;{\mathbb{i}}\;\theta_{1}}{\mathbb{e}}^{{- \pi}\;{\mathbb{i}}\;\theta_{2}}\sqrt{B_{k,l}}{\cos^{n - k - A_{k,l}}\left( {\pi\; x} \right)}{\sin^{k - A_{k,l}}\left( {\pi\; x} \right)} \times {\cos^{n - l - A_{k,l}}\left( {\pi\; y} \right)}{\sin^{l - A_{k,l}}\left( {\pi\; y} \right)} \times \left( {{{- {\cos\left( {\pi\; x} \right)}}{\sin\left( {\pi\; x} \right)}} + {{\cos\left( {\pi\; y} \right)}{\sin\left( {\pi\; y} \right)}}} \right)^{A_{k,l}}{F_{k,l}^{2}\left( {\theta_{1},\theta_{2}} \right)}} = {\frac{1}{2}{{\det\; M}}^{1/2}i^{k + l + A_{k,l}}{\mathbb{e}}^{{- \pi}\;{\mathbb{i}}\;\theta_{1}}{\mathbb{e}}^{{- \pi}\;{\mathbb{i}}\;\theta_{1}}{\mathbb{e}}^{{- \pi}\;{\mathbb{i}}\;\theta_{2}}\sqrt{B_{k,l}}{\cos^{n - k - A_{k,l}}\left( {\pi\; x} \right)}{\sin^{k - A_{k,l}}\left( {\pi\; x} \right)} \times {\cos^{n - l - A_{k,l}}\left( {\pi\; y} \right)}{\sin^{l - A_{k,l}}\left( {\pi\; y} \right)} \times \left( {{{\cos\left( {\pi\; x} \right)}{\sin\left( {\pi\; x} \right)}} + {{\cos\left( {\pi\; y} \right)}{\sin\left( {\pi\; y} \right)}}} \right)^{A_{k,l}}}}}} \right.}$where M is a sampling matrix of a rectangular grid, a quincunx grid, ora hexagonal grid.f _(k,l) ¹

F _(k,l) ¹ ;f _(k,l) ²

F _(k,l) ²Λ_(f)={(0,0), (0,n), (n,0), (n,n)}Λ_(g)={(k,1)}_(k=0, n;l=1, . . . , n-1)∪{(k,l)}_(l=0, n;k=1, . . . , n-1)Λ_(a)={(k,l)}_(k=1, . . . , n-1;l=1, . . . . , n-1)P_(n)={√{square root over (2)}f_(k,l) ¹}_((k,l)εΛ) _(f) _(∪Λ) _(g)∪{f_(k,l) ¹}_((k,l)εΛ) _(a) ∪{f_(k,l) ²}_((k,l)εΛ) _(a)

Lemma 2 (H.&S. Arai, 2008) The necessary and sufficient condition thatPn be a framelet filter relating to a rectangular grid, a quincunx grid,or a hexagonal grid is that B=(B_(k,l)) satisfies the followingcondition.

${\sum\limits_{k = 0}^{n}\;{\sum\limits_{l = 0}^{n}\;{\sum\limits_{j = 1}^{2}\;{{F_{k,l}^{j}\left( {\theta_{1},\theta_{2}} \right)}}^{2}}}} \equiv {{\det\; M}}$

<Method of Determining B=(B_(k,l)) Satisfying the Above Condition>

{(k,l): k=0, 1, . . . , n₀, l=s, . . . , n₀,} is ordered as follows.

μ=(k,l), ν=(k′,l′)

$K_{\mu,v} = {2^{3 - {4\; n} + {4\; k}}\left( {- 1} \right)^{l}{\sum\limits_{p = 0}^{k}\;\left\{ {\begin{pmatrix}{2\; k} \\{2\; p}\end{pmatrix}\begin{pmatrix}\begin{matrix}{\left\lbrack {\sum\limits_{q = 0}^{{2\; k} - {2\; p}}\;{\left( {- 1} \right)^{q}\begin{pmatrix}\begin{matrix}{{{- 2}\; k} -} \\{{2\; p} + {2\; n}}\end{matrix} \\\begin{matrix}{{2\; k^{\prime}} - {2\; p} +} \\{n - q}\end{matrix}\end{pmatrix}\begin{pmatrix}{{2\; k} - {2\; p}} \\q\end{pmatrix}}} \right\rbrack \times} \\{\left\lbrack {\sum\limits_{q = 0}^{{2\; p} + {2\; l} - {2\; k}}\;{\left( {- 1} \right)^{q}\begin{pmatrix}\begin{matrix}{{2\; p} + {2\; n} -} \\{{2\; k} - {2\; l}}\end{matrix} \\\begin{matrix}{{2\; l^{\prime}} + {2\; p} + n -} \\{{2\; k} - q}\end{matrix}\end{pmatrix}\begin{pmatrix}\begin{matrix}{{2\; p} +} \\{{2\; l} - {2\; k}}\end{matrix} \\q\end{pmatrix}}} \right\rbrack +}\end{matrix} \\{\left\lbrack {\sum\limits_{q = 0}^{{2\; k} - {2\; p}}\;{\left( {- 1} \right)^{q}\begin{pmatrix}\begin{matrix}{{{- 2}\; k} -} \\{{2\; p} + {2\; n}}\end{matrix} \\\begin{matrix}{{2\; l^{\prime}} - {2\; p} +} \\{n - q}\end{matrix}\end{pmatrix}\begin{pmatrix}{{2\; k} - {2\; p}} \\q\end{pmatrix}}} \right\rbrack \times} \\\left\lbrack {\sum\limits_{q = 0}^{{2\; p} + {2\; l} - {2\; k}}\;{\left( {- 1} \right)^{q}\begin{pmatrix}\begin{matrix}{{2\; p} + {2\; n} -} \\{{2\; k} - {2\; l}}\end{matrix} \\\begin{matrix}{{2k^{\prime}} + {2\; p} +} \\{n - {2\; k} - q}\end{matrix}\end{pmatrix}\begin{pmatrix}{{2\; p} + {2\; l} - {2\; k}} \\q\end{pmatrix}}} \right\rbrack\end{pmatrix}} \right\}}}$ ${\begin{pmatrix}K_{1,1} & \ldots & K_{1,{\frac{1}{2}{({n_{0} + 1})}{({n_{0} + 2})}}} \\\vdots & \ddots & \vdots \\K_{{\frac{1}{2}{({n_{0} + 1})}{({n_{0} + 2})}},1} & \ldots & K_{{\frac{1}{2}{({n_{0} + 1})}{({n_{0} + 2})}},{\frac{1}{2}{({n_{0} + 1})}{({n_{0} + 2})}}}\end{pmatrix}\begin{pmatrix}X_{1} \\X_{2} \\\vdots \\X_{\frac{1}{2}{({n_{0} + 1})}{({n_{0} + 2})}}\end{pmatrix}} = \begin{pmatrix}4 \\0 \\\vdots \\\; \\0\end{pmatrix}$ $\mspace{20mu}{B_{k,l} = \left\{ \begin{matrix}{2\; X_{s}} & {{s = {{\frac{1}{2}\left( {k - 1} \right)\left( {{2\; n_{0}} - k + 4} \right)} + 1}},{k = 1},\ldots\mspace{14mu},n_{0}} \\X_{s} & {{or}\mspace{14mu}{others}}\end{matrix} \right.}$

Theorem 3 (H.&S. Arai, 2008) B=(B_(k,l)) determined above satisfiesLemma 2. Therefore, Pn is a framelet filter relating to a rectangulargrid, a quincunx grid, or a hexagonal grid. Pn is referred to as apinwheel framelet of degree n. FIG. 54 is a diagram illustrating thefilters obtained by calculating the cyclic correlation product ofmaximum overlap pinwheel framelet filters at level 2 and an approximatefilter at level 1. FIG. 55 is a diagram illustrating each subband signalof the result obtained by performing the 2nd stage of maximal overlapMRA decomposition by a pinwheel framelet on a test image.

This is the end of the explanation of the present embodiment. In thismanner, according to the present embodiment, it is possible to providean illusion image generating apparatus, an illusion image generatingmethod, a printing medium manufacturing method, a program, and arecording medium capable of generating an illusion image from anarbitrary original image, a medium that displays an illusion image, andimage data for reproducing the illusion image. More specifically,according to the present invention, for example, if flyers, fans, cards,or the like are distributed on which the characters of a company's name,product name, or the like, figures, or the like that create a floatingillusion are printed, it is possible to increase the advertising effectfor the company or the like; therefore, the present invention is usefulin fields such as the advertising industry. Moreover, it is possible toprovide illusion images as entertainment products, such as a picturebook, or enjoy illusion images by floating greetings, names, or the likeon New Year's cards, Christmas cards, business cards, or the like;therefore, the present invention is extremely useful in toy-relatedfields, printing-related fields, and the like. Moreover, for cellphones, such as smartphones, touchscreen personal computers, or thelike, it is possible to provide an application with which, when a usercaptures a favorite image or character string or draws it on the screen,this can be converted to a floating illusion or a floating illusionimage thereof can be printed; therefore, the present invention isextremely useful also in software-related fields and the like. Moreover,if a floating illusion image is displayed on the screen, display, or thelike, pedestrians can see the image as if it is floating.

OTHER EMBODIMENTS

The embodiment of the present invention has been described above, andthe present invention can be implemented by various differentembodiments within the scope of the technical idea described in theclaims in addition to the above-described embodiment.

For example, an explanation is given of the case where the illusionimage generating apparatus 100 performs the processing in stand-alonemode as an example; however, the illusion image generating apparatus 100may perform the processing in response to a request from a clientterminal (cabinet different from the illusion image generating apparatus100) and return the processing results to the client terminal. Forexample, the illusion image generating apparatus 100 may be configuredas an ASP server, receive the original image data transmitted from auser terminal via the network 300, and return the reconstructed imagedata for the floating illusion image processed on the basis of thisoriginal image data to the user terminal.

Moreover, among the processings described in the embodiment, all or partof the processings described as automatic processing may be performedmanually and all or part of the processings described as manualprocessing may be performed automatically by well-known methods.

In addition thereto, the processing procedures, the control procedures,the specific names, the information including registered data of eachprocessing and parameters, such as retrieval conditions, the screenexamples, and the database configurations, described in the literatureand drawings above may be arbitrarily modified unless otherwiseindicated.

Furthermore, each component of the illusion image generating apparatus100 illustrated in the drawings is formed on the basis of functionalconcept, and is not necessarily configured physically the same as thoseillustrated in the drawings.

For example, all or any part of the processing functions that thedevices in the illusion image generating apparatus 100 have, andparticularly each processing function performed by the control unit 102,may be implemented by a CPU (Central Processing Unit) and a programinterpreted and executed by the CPU, or may be implemented as hardwareby wired logic. The program is recorded in a recording medium, whichwill be described later, and is mechanically read by the illusion imagegenerating apparatus 100 as necessary. Specifically, the storing unit106, such as a ROM and an HDD, or the like records a computer programfor providing instructions to the CPU in cooperation with the OS(Operating system) and for executing various processings. This computerprogram is executed by being loaded into a RAM and configures thecontrol unit in cooperation with the CPU.

Moreover, this computer program may be stored in an application programserver that is connected to the illusion image generating apparatus 100via the arbitrary network 300, and all or part thereof may be downloadedas necessary.

Furthermore, the program according to the present invention may bestored in a computer-readable recording medium and may be configured asa program product. The “recording medium” includes any “portablephysical medium”, such as a memory card, a USB memory, an SD card, aflexible disk, a magneto-optical disk, a ROM, an EPROM, an EEPROM, aCD-ROM, an MO, a DVD, and a Blue-ray Disc.

Moreover, the “program” refers to a data processing method written inany language and any description method and is not limited to a specificformat, such as source codes and binary codes. The “program” is notnecessarily configured unitarily and includes a program constituted in adispersed manner as a plurality of modules and libraries and a programthat implements its functions in cooperation with a different programrepresentative of which is an OS (Operating System). Well-knownconfigurations and procedures can be used for the specific configurationand reading procedure for reading a recording medium, the installationprocedure after reading a recording medium, and the like in each deviceillustrated in the present embodiment.

Various databases and the like (the framelet file 106 a to the imagedata file 106 b) stored in the storing unit 106 are a storage unit,examples of which is a memory device, such as a RAM and a ROM, a fixeddisk drive, such as a hard disk, a flexible disk, and an optical disk,and stores various programs, tables, databases, files for web pages, andthe like that are used for various processings or providing websites.

Moreover, the illusion image generating apparatus 100 may be configuredas an information processing apparatus, such as well-known personalcomputer and workstation, or may be configured by connecting anarbitrary peripheral device to the information processing apparatus.Moreover, the illusion image generating apparatus 100 may be realized byinstalling software (including program, data, and the like) that causesthe information processing apparatus to realize the method in thepresent invention.

A specific form of distribution/integration of the devices is notlimited to those illustrated in the drawings and it may be configuredsuch that all or part thereof is functionally or physically distributedor integrated, by arbitrary units, depending on various additions or thelike or depending on functional load. In other words, theabove-described embodiments may be performed by arbitrarily combiningthem with each other or the embodiments may be selectively performed.

REFERENCE SIGNS LIST

100 illusion image generating apparatus

102 control unit

102 a decomposing unit

102 b reconstructing unit

102 c floating illusion creating unit

102 d color space conversion unit

102 e illusion image output unit

104 communication control interface unit

106 storing unit

106 a framelet file

106 b image data file

108 input/output control interface unit

112 input device

114 output device

200 external system

300 network

The invention claimed is:
 1. A printed illusion image printed by a printer on a print medium, wherein a predetermined component is attenuated or amplified among components extracted and reconstructed by filters with respective orientations or components with respective orientations, which include wavelet components with respective orientations; the components compose an original image; and the illusion image creates an illusion of floating due to the movement of the image or the viewer, and appears to move differently from the actual movement accompanied by the movement of the viewer or the movement of the image.
 2. The printed illusion image according to claim 1, wherein: an illusion of wavering in a lateral direction is created when the movement is longitudinal; an illusion of wavering in a longitudinal direction is created when the movement is lateral; or both.
 3. The printed illusion image according to claim 1, wherein the illusion image has floating directions different from each other in image regions adjacent to each other.
 4. The printed illusion image according to claim 3, wherein: the image regions waver laterally in opposite directions to each other when the movement is longitudinal; or the image regions waver longitudinally in opposite directions to each other when the movement is lateral.
 5. The printed illusion image according to claim 1, wherein the print medium is paper or an OHP sheet.
 6. The printed illusion image according to claim 1, wherein the print medium is a flyer, a fan, a card, or a picture book.
 7. A printed illusion image printed by a printer on a print medium, wherein: the illusion image is a sum of subband signals; the subband signals are results of a multiresolution decomposition performed on original image data by a wavelet frame with orientation selectivity or a filterbank with orientation selectivity that is a set of an approximate filter with no orientation and a plurality of detail filters with respective orientations; a subband signal corresponding to at least one of detail filters with a predetermined orientation relative to a floating direction, in which an image is desired to be floated due to an illusion, among the detail filters is attenuated or amplified; and the illusion image creates an illusion of floating due to the movement of the image or the viewer, and appears to move differently from the actual movement accompanied by the movement of the viewer or the movement of the image.
 8. The printed illusion image according to claim 7, wherein: an illusion of wavering in a lateral direction is created when the movement is longitudinal; an illusion of wavering in a longitudinal direction is created when the movement is lateral; or both.
 9. The printed illusion image according to claim 7, wherein the illusion image has floating directions different from each other in image regions adjacent to each other.
 10. The printed illusion image according to claim 9, wherein: the image regions waver laterally in opposite directions to each other when the movement is longitudinal; or the image regions waver longitudinally in opposite directions to each other when the movement is lateral.
 11. The printed illusion image according to claim 7, wherein the print medium is paper or an OHP sheet.
 12. The printed illusion image according to claim 7, wherein the print medium is a flyer, a fan, a card, or a picture book.
 13. A non-transitory computer-readable recording medium on which an image data for displaying an illusion image is recorded, the illusion image produced from original image data by: obtaining subband signals by performing a multiresolution decomposition on the original image data by a wavelet frame with orientation selectivity or a filterbank with orientation selectivity that is a set of an approximate filter with no orientation and a plurality of detail filters with respective orientations; attenuating or amplifying a subband signal corresponding to at least one of detail filters with a predetermined orientation relative to a floating direction, in which an image is desired to be floated due to an illusion, among the detail filters; and reconstructing an image by summing the subband signals; wherein the illusion image creates an illusion of floating due to the movement of the image or the viewer, and appears to move differently from the actual movement accompanied by the movement of the viewer or the movement of the image.
 14. The non-transitory computer-readable recording medium according to claim 13, wherein: an illusion of wavering in a lateral direction is created when the movement is longitudinal; an illusion of wavering in a longitudinal direction is created when the movement is lateral; or both.
 15. The non-transitory computer-readable recording medium according to claim 13, wherein the illusion image has floating directions different from each other in image regions adjacent to each other.
 16. The non-transitory computer-readable recording medium according to claim 15, wherein: the image regions waver laterally in opposite directions to each other when the movement is longitudinal; or the image regions waver longitudinally in opposite directions to each other when the movement is lateral.
 17. The non-transitory computer-readable recording medium according to claim 13, wherein the image data is two-dimensional image data in a raster format or a vector format. 